Random Variable Support
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See: Random Variable, Function Domain, Sample Space.
References
2006
- (Dubnicka, 2006c) ⇒ Suzanne R. Dubnicka. (2006). “Random Variables - STAT 510: Handout 3." Kansas State University, Introduction to Probability and Statistics I, STAT 510 - Fall 2006.
- MATHEMATICAL DEFINITION: A random variable [math]\displaystyle{ X }[/math] is a function whose domain is the sample space S and whose range is the set of real numbers [math]\displaystyle{ R }[/math] = {x : −∞ < [math]\displaystyle{ x }[/math] < ∞.}. Thus, a random is obtained by assigning a numerical value to each outcome of a particular experiment.
- WORKING DEFINITION: A random variable is a variable whose observed value is determined by chance.
- NOTATION: We denote a random variable [math]\displaystyle{ X }[/math] with a capital letter; we denote an observed value of [math]\displaystyle{ X }[/math] as [math]\displaystyle{ x }[/math], a lowercase letter.
- TERMINOLOGY : The 'support of a random variable [math]\displaystyle{ X }[/math] is set of all possible values that [math]\displaystyle{ X }[/math] can assume. We will often denote the support set as SX. If the random variable [math]\displaystyle{ X }[/math] has a support set SX that is either finite or countable, we call [math]\displaystyle{ X }[/math] a discrete random variable.